Information Spreading in Diffusion Models from Effective Field Theory

Abstract

We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.

This work was previously presented at the Scientific Methods for Understanding Deep Learning Workshop at ICLR 2026. 14 pages + appendices. Code available at: https://github.com/NavonilNeogi/MutualInfoEFTDiffusionModels